Question

Hello to the esteemed Rabbi, good evening.
In tractate Ketubot (72b), there in the chapter HaMadir, there is a passage about betrothing a woman, where the husband stipulates that this is on condition that the woman has no vows, and in the end it turns out that she did have vows upon her. The law is that she is not betrothed, as is known.
And later in that passage (74a) it says that even if she does have vows, if she went to a sage and he released them, the betrothal takes effect. (As opposed to a physician in the case of physical defects.)
Because a sage uproots the vow retroactively, and it turns out after the fact that already from the time of the betrothal, in the end there were no vows upon her. (And Tosafot there explain this specifically in a case where it was not with the husband's knowledge, which is straightforward.)
 
My question—in this kind of case, when does the betrothal take effect? On the face of it, from the time the husband betrothed her…
But I have a feeling that this is not simple at all. Because it seems that a new dimension of time is opened up here.
(For example, if Jacob betrothed her on Sunday, on condition that she has no vows upon her, and only on Tuesday did she go to a sage who released her vow [unrelated to Jacob], seemingly the betrothal takes effect retroactively already from Sunday.)
 
Let us sharpen the case: between Sunday and Tuesday she married another man, let's say his name is Dan, and this was on Monday.
Is it the case that retroactively she was never betrothed to Dan at all? (Because, as it were, retroactively Jacob's betrothal preceded Dan's. But there is something deceptive here, because in the end at the time she married Dan on Monday, she was not married to Jacob according to Torah law, and that is indeed when Dan's betrothal takes effect.)